Tags // Reasoning

Deductive vs inductive arguments

Mastering the art of picking out premises and conclusions is the first step toward good analytical thinking, but we must also think about whether the premises really do support their conclusions. Making that sort of determination requires that we think a little bit about the different kinds of arguments. There are several ways of categorizing arguments, but for our purposes, we can distinguish all arguments into one of two types: deductive and inductive.

Deductive argument: an argument whose premises make its conclusion certain

Inductive argument: an argument whose premises make its conclusion likely

(Note: Some dictionaries – and even some older logic texts – define deductive arguments as arguments that reason from the general to the specific and inductive arguments as those that reason from the specific to the general. That particular usage of the terms is obsolete.)

The difference between deductive and inductive arguments is easiest to see by way of examples.

Smith owns only blue pants and brown pants. Smith is wearing a pair of his pants today. So Smith is wearing either blue or brown pants today.

This is an instance of a deductive argument. We can tell that the argument is deductive because the two premises (that is, the first two sentences) guarantee the truth of the conclusion. If the two premises really are true, then there is no possible way that the conclusion could be false. Here’s another example:

The soccer game is on either Thursday or Friday. I just found out that the game is not on Thursday, so the game must be on Friday.

Again, this is a deductive argument, for the truth of the premises guarantees the truth of the conclusion. Contrast those examples with this one:

January has always been cold here in Siberia. Today is January 14, so it is going to be another cold day in Siberia.

This argument is inductive. The premises makes the conclusion likely, but they do not guarantee that the conclusion is true. To put the point another way, it is possible that the premises of this argument could be true and the conclusion could still be false. One can, for example, imagine a freak warm day in Siberia on January 14. But one cannot imagine that Smith owns only brown pants and blue pants, that he is wearing his own pants and that his pants are not brown or blue. To make the conclusion about the color of Smith’s pants false, one has to make one of the premises false. But one can make the cold day in Siberia claim false while keeping the premises true. Here is one more:

The local branch of Wachovia Bank was robbed yesterday. Jenny needed money to pay off her gambling debts. She just bought a gun two days ago, and I saw her hanging around the local Wachovia Bank yesterday morning. Today the bookie’s goons stopped looking for Jenny. So Jenny robbed Wachovia Bank yesterday.

This is the sort of inductive argument that should be familiar to anyone who has ever watched an episode of “Law & Order.” Again, though, as anyone who has seen “Law & Order” can attest, these sorts of inductive arguments can be (and frequently are) wrong. Even if all the premises are true, it is still possible that the conclusion is false.